It appears to me that the US-Japan Tax Treaty says that your pension is taxable in the US IF you are not Japanese nationals (we have no idea if you are US or Japanese citizens).
Please see Articles 17 and 18 in the US-Japan Income Tax Treaty of 2003.
One could assume that if your foreign pension is taxable in the US, then the exclusion rules in New Jersey should apply to it.
Please note that reading Tax Treaties is a specialized science and I do not have nearly as much experience in this as @pk and I encourage you to seek an answer from @pk as a follow up.
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